(b) 3x2 14x + 10 = 0

-3-

4. Form the quadratic equations which roots are :

(a) 1 , 7

12

(b) 4 ,

5. Given that m and n are roots of the quadratic equation 2x2 11x 6 = 0 , form a quadraticequation with roots 3m and 3n .2.3 Types of the Roots of the Quadratic Equation1. The conditions for the nature of the roots of quadratic equations are( a ) two real and distinct roots : b2 4ac > 0( b ) two real and equal roots : b2 4ac = 0( c ) no real roots : b2 4ac < 0( d ) two real roots : b2 4ac 02. ( a ) If a straight line intersects a curve at two distinct points, the conditionb2 4ac > 0 is applied.( b ) If a straight line touches a curve at only one point, the condition b2 4ac = 0is applied.( c ) If a straight line does not meet a curve, the condition b2 4ac < 0 is applied.b2 4ac > 0